Question 338826
Th measure of an interior angle (a) of a regular polygon of n sides is given by:
{{{a = (n-2)180/n}}} Set this equal to 170 and solve for n.
{{{170 = (n-2)180/n}}} Multiply both sides by n.
{{{170n = (n-2)180}}} Simplify the right side.
{{{170n = 180n-360}}} Subtract 170n from both sides.
{{{0 = 10n-360}}} Add 360 to both sides.
{{{360 = 10n}}} Finally, divide both sides by 10.
{{{36 = n}}}
The regular polygon has 36 sides.